Solve for $x$ and $y$ using elimination. ${-2x-3y = -25}$ ${2x+5y = 39}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $2y = 14$ $\dfrac{2y}{{2}} = \dfrac{14}{{2}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {-2x-3y = -25}\thinspace$ to find $x$ ${-2x - 3}{(7)}{= -25}$ $-2x-21 = -25$ $-2x-21{+21} = -25{+21}$ $-2x = -4$ $\dfrac{-2x}{{-2}} = \dfrac{-4}{{-2}}$ ${x = 2}$ You can also plug ${y = 7}$ into $\thinspace {2x+5y = 39}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(7)}{= 39}$ ${x = 2}$